A triangular gap of size two in a sea of dimers on a 60^∘ angle

2014/05/16 by Mihai Ciucu, Ilse Fischer
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #math.CO #math.MP

paper · pdf

published as J. Phys. A: Math. Theor. 45 (2012), 494011 · 21 pages. arXiv admin note: substantial text overlap with arXiv:1403.0925

arxiv created 2014/05/16 · arxiv updated 2014/05/19

Abstract

We consider a triangular gap of side two in a 60^∘ angle on the triangular lattice whose sides are zig-zag lines. We study the interaction of the gap with the corner as the rest of the angle is completely filled with lozenges. We show that the resulting correlation is governed by the product of the distances between the gap and its five images in the sides of the angle. This provides a new aspect of the parallel between the correlation of gaps in dimer packings and electrostatics developed by the first author in previous work.

Citations

• A triangular gap of size two in a sea of dimers in a 90^∘ angle with mixed boundary conditions, and a heat flow conjecture for the general case